Friends,
I would think this has been covered before, but I am unable to find anything on it:
The locus of the centers of all circumhyperbolas passing through X(1) and a point on the Euler line is an ellipse with center X(1125). It passes through X(11) (center of Feuerbach Hyperbola) and X(1015) (Exsimilicenter of Moses Circle and Incircle). Are there any other Kimberling centers on this ellipse? I have checked the centers of circumhyperbolas passing through X(1) and Euler line points up to X(297), and have not found any. X(1015) is the center of hyperbola {A,B,C,X(1),X(2)}. The hyperbola {A,B,C,X(1),X(3)} also passes through X(29), and its center is not a Kimberling center.
Is anything else known about this ellipse?
Regards,
B. Randy Hutson
I would think this has been covered before, but I am unable to find anything on it:
The locus of the centers of all circumhyperbolas passing through X(1) and a point on the Euler line is an ellipse with center X(1125). It passes through X(11) (center of Feuerbach Hyperbola) and X(1015) (Exsimilicenter of Moses Circle and Incircle). Are there any other Kimberling centers on this ellipse? I have checked the centers of circumhyperbolas passing through X(1) and Euler line points up to X(297), and have not found any. X(1015) is the center of hyperbola {A,B,C,X(1),X(2)}. The hyperbola {A,B,C,X(1),X(3)} also passes through X(29), and its center is not a Kimberling center.
Is anything else known about this ellipse?
Regards,
B. Randy Hutson
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